Using NaOH@Graphene oxide-Fe3O4 as a magnetic heterogeneous catalyst for ultrasonic transesterification; experimental and modelling

Burning fossil fuels causes toxic gas emissions to increase, therefore, scientists are trying to find alternative green fuels. One of the important alternative fuels is biodiesel. However, using eco-friendly primary materials is a main factor. Sustainable catalysts should have high performance, good activity, easy separation from reaction cells, and regenerability. In this study, to solve the mentioned problem NaOH@Graphene oxide-Fe3O4 as a magnetic catalyst was used for the first time to generate biodiesel from waste cooking oil. The crystal structure, functional groups, surface area and morphology of catalyst were studied by XRD, FTIR, BET, and FESEM techniques. The response surface methodology based central composite design (RSM-CCD) was used for biodiesel production via ultrasonic technique. The maximum biodiesel yield was 95.88% in the following operation: 10.52:1 molar ratio of methanol to oil, a catalyst weight of 3.76 wt%, a voltage of 49.58 kHz, and a time of 33.29 min. The physiochemical characterization of biodiesel was based to ASTM standard. The magnetic catalyst was high standstill to free fatty acid due to the five cycle’s regeneration. The kinetic study results possess good agreement with first-order kinetics as well as the activation energy and Arrhenius constant are 49.2 kJ/min and 16.47 * 1010 min−1, respectively.


Experimental design
In order to enhance the process of optimization of biodiesel yield, the central composite design (CCD) based on response surface methodology (RSM) was employed.The study focused on three independent variables: catalyst weight (A), methanol to oil molar ratio (B), time (C), and ultrasonic frequently (D), while the dependent variable or response was biodiesel yield.The weight of the catalyst was kept stable with low variations during the transesterification reaction and was not considered as a factor.Table 1 outlines the lower and upper levels for each independent factor and shows their codes.To determine absolute errors, thirty experiments were conducted, with six replication sets at central points, such as eight axial, sixteen factorial points, and six central.The results of these experiments are presented in Table 3.
The yield of biodiesel, denoted as Y, is established through regression programming by computing.These coefficients pertain to the constant (α 0 ), interaction factors (α ij ), quadratic (β ii ), and linear (α i ), respectively.X i and X j are considered independent variables while ε denotes the error.The adjusted R-squared (R 2 adj ) and R squared (R 2 ) were calculated by Eqs. ( 3) and ( 4), respectively 34 .
where SS value is the sum of squared and the amount of DF is the degree of freedom.

Kinetic study
A kinetic model can be utilized to determine the rate constant and activation energy for the production of biodiesel from waste cooking oil.The study kept the reaction parameters constant, including catalyst weight, methanol to oil molar ratio, time, and ultrasonic frequency, but varied the temperatures (45, 55, and 65 °C).Biodiesel yield was measured by online product sampling at specific intervals.The lowest temperature of 45 °C was chosen due to the sluggish production of glycerol, while the highest temperature of 65 °C was selected as it was near the boiling point of methanol 35 .The first-order rate equation show in the Eq. ( 5).
(2)  www.nature.com/scientificreports/TG represents the triglyceride's concentration, K shows the constant rate (min −1 ), and t represents the time taken for the reaction.The following equation can be used to measure Eq. ( 5): where TG 0 and TG are the primary concentration of triglyceride (%) and the terminal concentration (%), respectively.the conversation of factor X was showed by Eq. ( 7): The K (min −1 ) for the transesterification in each of temperatures can be calculated by \the data got from the Eq. ( 8): The Arrhenius equation (Eq.( 9)) shows the energy of activation, applying information of constant speed and temperature according to the data got from the kinetic experimental.
where K and A are the velocity constant and Arrhenius constant, respectively.The E a is the activation energy (J/ mol), R is the universal gas constant (J/mol/K) and T is absolute temperature (K) 36 .

Properties of biodiesel
The physiochemical characterization of biodiesel from waste cooking oil like cloud point (ASTM D 2500), flash point (ASTM D 93), pour point (ASTM D 97), kinematic viscosity at 40 °C (ASTM D 445), density at 15 °C (ASTM D 1298), iodine value (ASTM D 874), cetane number, saponification value (ASTM D 97) were determined by the method of ASTM standards.

Study of and structural, thermal properties of magnetic catalyst
Morphological and elemental analysis Morphological structure of pure GO, GO-Fe 3 O 4 , and NaOH@GO-Fe 3 O 4 as magnetic heterogeneous catalyst after immobilizing NaOH have showed in Fig. 3.According to the FESEM images for pure GO, the morphological of GO layers were ruffled and twisted across texture.Shemshani et al. 37 believed that a functional oxygenated groups cause these structure.In addition, the thin and flexible layers of raw GO are easily seen.In Fig. 3b, the spherical shape of Fe 3 O 4 nanoparticles was observed on GO sheets.As well as they are uniformly scattered and twisted to both the inner and surface of GO layers.These results have good understanding with another reports 38,39 .It can be clearly seen that in Fig. 3c, the natural magnetic properties of Fe 3 O 4 nanoparticles have spherical-shaped of exists as agglomerates.In addition, after calcination of NaOH, they have needle-shaped crystals on the surface and inner of GO sheets.

Determining crystal structural
In order to study molecular vibration of various functional groups of pure GO, GO-Fe 3 O 4 , and NaOH@GO-Fe 3 O 4 FTIR analysis was used and showed in Fig. 4. The epoxy (C-O) group of pure GO has main peak at 1044 cm −1 and C-O-C groups has a main peak at and 1415 cm −1 , respectively.The C=C bands in aromatic groups have a peak at 1624 cm −1 .The C=O carboxyl groups on GO layers have a peak at 1721 cm −1 .The board and main peak which observes at 3431 cm −1 related to the stretch and binding vibration of -OH groups.FTIR analysis confirmed that GO layers have different special functional groups on their inner layer and surface, these functional groups assist to create binding sites with other materials like Fe 40 .These results are similar to the FTIR spectra of GO which are reported by other researchers 15,16 .
Although all peaks of raw GO are observed in the FTIR spectrum of GO-Fe 3 O 4 which indicated after immobilization Fe, the structure of GO does not change, however, chemical deposition of Fe 3 O 4 nano particles on the GO layers declines severity of the peaks.The GO-Fe 3 O 4 showed following main peaks: the carbonyl, C=C aromatic groups, and -OH groups have main peaks at 1415 cm −1 , 1621 cm −1 , and 3424 cm −1 , respectively.The peak at 1060 cm −1 which related to the C-O stretching vibration of epoxy groups.The specific and sharp peak at 567 cm −1 assigned to Fe-O with the stretching vibration.Based to the FTIR analysis results, the GO surface was improved by Fe 3 O 4 and the experimental results was similar to other reports 41,42 .
The same peaks GO-Fe 3 O 4 peaks with a light difference are observed in the FTIR spectra of NaOH@ GO-Fe 3 O 4 .The FTIR spectra of magnetic catalyst possess the peaks at 3426 cm −1 , 1636 cm −1 , 1365 cm −1 , and 1052 cm −1 which related to the -OH, C=C, carbonyl, and C-O groups, of pure GO, respectively.As well as, the specific peak observed at 575 cm −1 related to the Fe-O groups.In FTIR spectra of magnetic catalyst, the maiden peak was appeared at 1649 cm −1 corresponded to the -OH groups.The peaks which appeared at 1429 cm −1 and 877 cm −1 can be related to the O-Na deformation and plan bending of O-Na 43 .The peak at 575 cm −1 associated to the Fe-O-Fe in Fe 3 O 4 .According to the FTIR analysis results, after immobilization of NaOH, although the morphological and surface of GO-Fe 3 O 4 as magnetic catalyst support was changed, NaOH@GO-Fe 3 O 4 magnetic catalyst was successfully generated.
The crystal structure of pure GO, GO-Fe 3 O, and NaOH@GO-Fe 3 O 4 (Fig. 5) was studied by the XRD analysis.The single sharp peak clearly seen at 2θ = 12.8° with d-spacing of 7.02 Å corresponded to the crystal face of GO 44 .The characteristic peaks of GO-Fe 3 O 4 with low intensity were appeared at 30.72°, 35.6°, 42.44°, 57.28°, and 61.6° which showed Fe 3 O 4 magnetic nano particles with the cubic spinel crystal phase (JCPDS Card.PDF No. 85-1436) 20 .While the severity of GO peak at 2θ = 12.5° was decline significantly.This is because after the coating of Fe 3 O 4 nano particles, GO sheets hardly stack on together to prepare crystalline structure 45 .All in all, the board small peak illustrated that the synthesis of GO-Fe 3 O 4 was successfully.The GO-Fe 3 O 4 have similar peaks with NaOH@GO-Fe 3 O 4 .But some peaks were observed at 18.2°, 30.0°, 33.36°, 35.52°, 42.80°, 53.72°, 57.28°, 63° which were related to the NaOH@GO-Fe 3 O 4 .Deng et al. 46 announced that the peaks at 2θ = 31.0°,35.52°, 42.80°, and 57.28° were assigned to the maghemite or magnetite, the peaks at 2θ = 52.5°and 63° were associated to the hematite, and the magnetic composite structure has peaks at 2θ = 19.2°and 34.36°.The new peak observed at 2θ value of 33.36° was related to the Na 2 O phase as well 47 .Calcination process of catalyst causes that the NaOH molecules converted to the Na 2 O, therefore, magnetic catalyst have high alkaline characterization.In order to measure the particles size of magnetic catalyst the Debye-Scherrer equation (Eq.10) was used:  where S is the size of crystalline.λ , β and θ are x-ray wavelength line, width at half highest of the peaks of a radian and Bragg angle, respectively.The nanoparticles size of NaOH@GO-Fe 3 O 4 is an average size 14.2\2 nm.

Investigating surface area and pore volume
The specific surface area (S BET ), total porosity of particles (V p ), average pore diameter (nm) of NaOH@GO-Fe 3 O 4 magnetic catalyst were studied by BET analysis.The results of BET analysis are displayed in Table 2.The general surface area of solid catalyst was 20.07 m 2 /g. the mean pore diameter and general porosity of particles were obtained 14.05 nm and 15.06 cm 3 /g, respectively.Based on the IUPAC categorize, NaOH@GO-Fe 3 O 4 has mesoporous pores 48 .
All in all, WCO as a basic feedstock for biodiesel may be a low-cost and plenteous resource that can diminish the cost of the biodiesel production process.This feedstock, also, is not in the human chain.It can keep up a key separate the competition for arable arrive and water resources that are related to consumable oils as well 49 .It can diminish the characteristic influence of misuse exchange and the outpouring of green gasses, as the carbon contained in misused cooking oil is to an awesome degree biogenic and renewable 50 .NaOH@graphene oxide-Fe 3 O 4 may well be an attractive magnetic heterogeneous catalyst that can be successfully separated by magnet, keeping up a vital separate from the issues of catalyst loss, wastewater generation, and soap formation that are common with homogeneous catalysts It incorporates a catalytic development and selectivity, as the NaOH gives the fundamental regions for the transesterification, though the graphene oxide and Fe 3 O 4 overhaul the consistent quality, diffusing, and alluring properties of the catalyst.It can work underneath smooth reaction conditions, such as mild reaction temperature, low catalyst weight, and low oil-to-methanol molar ratio, diminishing essentialness utilization and advancing the biodiesel resign. 51.

Response surface methodology (RSM) analysis
The aim of the study was to assess the impact of varying the independent factors of the molar ratio between methanol and oil (A), catalyst weight (B), reaction time (C), and ultrasound frequency (D) on biodiesel yield (%). Using the central composite design method, thirty experiments were conducted to investigate the value of independent parameters and their interactions on biodiesel yield, as outlined in Table 3 upon evaluating various models, operational parameters have quadratic and significant model, with the best regression model expressed in Eq. ( 3) based on the experimental data.The coefficient of determination (R 2 ) was used to determine the state of the quadratic model.The value of R 2 was 0.9927, predicted-R 2 was 0.9859, and the Adjusted-R 2 value was 0.9620.The high value of R 2 proves that the model could measure the biodiesel yield verified by the mathematical equation.A good agreement was seen between the experimental and predicted biodiesel yield as well.
The objective of this study was to evaluate the influence of various independent variables on biodiesel yield (%), including A, B, C, D. The central composite design method was used to perform 30 experiments and assess the individual variables and their interactions on biodiesel yield (Table 3).The Analysis of variance (ANOVA) was used to calculate interaction between independent parameters such as catalyst weight (3-5 wt%), methanol to oil molar ratio (5:1 to 20:1), ultrasonic frequency (35-55 kHz), and reaction time (15-45 min) (Table 4), and determine the optimal conditions.Variables with higher F-values and smaller P-values has a necessary effect on biodiesel production as a response, while AD did not.The insignificant lack of fit further confirmed the model's adequacy, and the coefficient of variance (CV) demonstrated its high accuracy.
Figure 6a displays both the predicted and actual Biodiesel yield values, while Fig. 6b shows a normal probability plot indicating that the data is normally distributed 48 .If the curve follows an S-shape, it is incorrect to use the model, and an additional response transformation is necessary [48).The outlier t plot for all response runs is presented in Fig. 6c, which identifies runs with high residuals.The majority of residuals should fall within + 3.87982 and -3.87982 that indicate two types of error including operational and positional errors in the empirical data and mathematical model, respectively.As no data points fall outside this range, the results suggest that all data are compatible with this model.Figure 6d displays the studentized residuals against predicted response, which should be randomly distributed to demonstrate that changes in primary observations not relevant to the amount of response.All data do not use particular patterns for scattering in Fig. 6d supports the suggested model as a precise representation of the transesterification process.

Effects of operating independent factors on transesterification reaction
The biodiesel yield is impacted by two independent variables, with Fig. 9 displaying 3D and 2D plots.The methanol oil molar ratio serves as the primary factor influencing the biodiesel yield.As demonstrated in Fig. 7a,b,f, an enhancing in this independent factor causes that biodiesel yield increases, with a maximum of 95.88% achieved at a ratio of 10.52:1.However, by enhancing methanol to oil molar ratio higher than optimum condition lead to biodiesel yield decreases 52 The catalyst weight (B) is a primary factor in transesterification reaction.The value of the weight of NaOH@ GO-Fe 3 O 4 was changed from 3 to 5wt%.Based on the results of Fig. 7a,c,d.The NaOH@GO-Fe 3 O 4 considers as an active catalyst due to high alkali sites that have positive effect on the interaction between triglyceride oil molecules and methanol molecules that cause biodiesel produced with highest yield [71).Therefore, only 3.76 g  www.nature.com/scientificreports/ of alkali magnetic catalyst could generated biodiesel with high yield of 95.88%.However, increasing catalyst more than 3. 76 g has a negative effect on the transesterification reaction due to mass transfer resistance, All in all, when the final biodiesel yield decreases, the reaction mixture was viscose, and the mixture agents harder 47 .The results presented in Fig. 7b,c,e demonstrate that the maximum response was obtained after a certain period of time was obtained after a certain period of time.Increasing the reaction time from 5 to 33.29 min resulted in an increasing biodiesel yield to 95.88%.During the initial stages of the reaction, methanol reacted with the oil molecules at a slow rate.However, after 33.29 min, the reaction rate improved and more biodiesel www.nature.com/scientificreports/generated because the triglyceride oil molecules have sufficient time to participate in the transesterification reaction.The transesterification rate enhanced due to the molecules reacting together.The biodiesel yield, however, declined after the optimum reaction time due to ester hydrolysis and the reversible reaction of transesterification.Therefore, the optimum reaction time was chosen at 33.29 min.Figure 7d-f shows the Ultrasonic frequently impacts multiple from 35 to 55 kHz.Biodiesel yield increased to 95.88% at the Ultrasonic frequently of 49.58 kHz.Increasing Ultrasound frequency can raise the adsorption rate and indeed, the rate of CH 3 O − ions generation.Convection that was produced by ultrasound assists in the scattering of the organic phase and aqueous phase into each other.Therefore, the formation of an emulsion causes a high interfacial area.In addition, cavitation bubbles provide convection via the production of acoustic waves that generate emulsion of the two phases.Although the magnitude of these waves declines significantly at higher temperatures, it could be attended that the level of the convection level in the medium should decrease with temperature 53 so 49.58 kHz was selected as the optimum ultra-frequency.

Optimization of biodiesel production
The RSM-CCD with four independent factors was utilized to optimize the factors within the determined range, taking into account the standard error (StdErr) present in the numerical model.Figure 8 illustrates the optimal values of each factors among the highest and lowest limits.The second-order quadratic polynomial model was employed to determine both the highest biodiesel yield and the optimum factors, which was predicted to be 95.88%.The optimal conditions for achieving this yield were a 10.52:1 molar ratio of methanol to oil, a catalyst weight of 3.76 wt%, a voltage of 49.58 kHz, and a time of 33.29 min.However, the actual yield obtained was very close to the predicted value.

Characterization of biodiesel
The characteristics of fuel are highly influential in determining how the addition of biodiesel affects diesel engine performance, combustion, and emissions.Table 5 outlines key parameters, including pour point, cloud point, flash point, ash content, Saponification Value, Iodine value, acid value, viscosity, density, and cetane number.Viscosity and density are particularly important as they impact on efficiency of both combustion of fuel, and fuel injection.The amount of saponification indicates the acyl group quantity in the oil phase, while the position of unsaturation in oil was measured by iodine value.The cetane number is a crucial parameter that gauges combustion lag cycle in diesel engines.The ideal biodiesel should meet ASTM standards and exhibit a high flash point, in addition, high cloud point and low pour point perform optimally in various climate conditions.

Kinetic study
Figure 9 illustrates the biodiesel yield (%) as a response against reaction time at various temperatures from 25 to 65.Clearly, the transesterification rate was gradual at the first step of the process, but the rate intensely enhanced with passing time.Therefore, biodiesel yield is increased linearly 54 .For a stable reaction rate module at various temperatures (25 °C, 45 °C, and 65 °C), the plot between − Ln(1 − X) versus reaction time displays the biodiesel yield as can be seen in Fig. 10.A linear equation is observed in all temperatures.Therefore, it concluded that biodiesel production is a pseudo-first-order reaction.For all curves, the R 2 values (25 °C-0.2329,45 °C-0.3146, and 65 °C-0.4646)were more than 0.9 which proved the high accuracy of the porposed correlations.The activation energy of process is 49.2 kJ/min and Arrhenius constant of transesterification is 16.47 * 10 10 min −1 .

Catalyst regeneration
Regeneration catalyst is a significant factor in the transesterification reaction, catalyst should be recycled as many times without significant function (Fig. 11).At the end of the reaction, magnetic catalyst was separated by magnet, then washed with n-hexane in order to remove impurities, next dried at oven over night, finally used for biodiesel production.Based to the regeneration process, NaOH@GO-Fe 3 O 4 as a magnetic catalyst reused five times without decline significantly.Tan et al. 55 reported that catalyst surface was recovered by larger molecular oil, therefore active sites deactivate and biodiesel yield declined.

Comparison of results with other studied
The optimum reaction conditions and final biodiesel yield of this study and other reports that used magnetic GO as a base of heterogeneous catalysts were summarized in the Table 6.From the comparison, it is concluded that the NaOH@GO-Fe 3 O 4 as a magnetic catalyst could generate biodiesel in a short time (33.29 min).That is because the ultrasonic method is a technique that uses high-frequency sound waves to create bubbles in the liquid mixture of oil and alcohol.These bubbles collapse violently, generating intense heat and pressure that accelerate the transesterification reaction.This process enhances the mass transfer and mixing of the immiscible reagents, reduces the catalyst loading and reaction temperature, and increases the biodiesel yield and conversion rate.Therefore, the consumption of energy significantly decreased.By using only 3.76 wt% magnetic catalyst, biodiesel was produced with a high yield (95.88%) as well.The consumption of methanol to oil was 10:1 molar ratio so low reactive materials such as methanol and catalyst were used.At the end of each cycle, the magnetic catalyst was separated by an external magnet, therefore, the cost of using a centrifuge or anything was eliminated which had a significant effect on the final cost of biodiesel as a product.By considering that NaOH@GO-Fe 3 O 4 was able to be reused five times, this catalyst has economic viability and is able to be used on a large scale.

Conclusion
In this research, the optimization of the biodiesel production from WCO using the NaOH@GO-Fe 3 O 4 as magnetic catalyst was performed via the RSM-CCD.The NaOH@GO-Fe 3 O 4 has an alkali natural because NaOH changes the GO structures, when Na + ions immobilized with GO structure and strong chemical bonds was created by oxygenated functional groups of GO structure.The highest biodiesel yield was 95.88% subject the optimum conditions of 3.76 wt% NaOH@GO-Fe 3 O 4 , methanol to oil molar ratio of 10.52:1, the reaction time of 33.29 min, and ultrasonic frequency of 49.58 kHz.The actual experimental results showed NaOH@GO-Fe 3 O 4 showed high activity and stability in biodiesel production.As R 2 , pre-R 2 , and adj-R 2 had high value, it proved than the proposed mathematical model by RSM-CCD possessed a high accuracy to evaluate the biodiesel yield as a process response According to the kinetic results, the activation energy of the process was 49.2 kJ/min and Arrhenius constant was 16.47 × 10 10 min −1 .The NaOH@GO-Fe 3 O 4 catalyst could generate five times, with average biodiesel yield 86.6%.The physicochemical characterization of the biodiesel which produce under optimum condition had a good contract with the ASTM standard, therefore, producing biodiesel via NaOH@GO-Fe 3 O 4 from WCO can performed in industrial scale due to low cost and high efficiency of catalyst.

Figure 2 .
Figure 2. Scheme of biodiesel production via ultrasonic method.

Figure 7 .
Figure 7.The 3D surface and 2D contour plots of interaction between (a) catalyst weight and methanol to oil molar ratio, (b) reaction time and methanol to oil, (c) catalyst weight and reaction time, (d) ultrasonic frequency and catalyst weight, (e) ultrasonic frequency and reaction time, (f) Ultrasonic frequently and methanol to oil.

Figure 8 .
Figure 8. Reaction condition of transesterification reaction under optimum condition.

Figure 9 .Figure 10 .
Figure 9. Plot of biodiesel yield as response versus reaction time at different temperatures.

Figure 11 .
Figure 11.(a) Reusability of catalyst, (b) NaOH@GO-Fe 3 O 4 as a magnetic catalyst was separated by magnet from reaction mixture.

Table 1 .
Lower and high levels of independent factors Based on BBD.

Table 3 .
RSM based CCD for four independent factors.

Table 4 .
ANOVA for Quadratic model.

Table 5 .
Physicochemical properties of ASTM D6751 and biodiesel.

Table 6 .
Comparison of optimum reaction conditions and biodiesel yield in literature.